The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Poljak in 1966. It is the natural extension of the class of the strongly convex functions and their applications emcompasses different problems from mathematical sciences, economics and engineering among others. In this talk, we present an overview on strongly quasiconvex functions from the open question regarding the existence of solutions for the minimization problem formulated by Poljak in 1966 until its solution in 2022. As a consequence, we present two applications in continuous optimization; An study of the proximity operator and its applications in proximal point algorithms and a generalized subdifferential for studying nonsmooth strongly quasiconvex functions and its applications in subgradient methods.